Optimal. Leaf size=23 \[ -\frac {1}{100} (1-x)^{100}+\frac {1}{101} (1-x)^{101} \]
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Rubi [A]
time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45}
\begin {gather*} \frac {1}{101} (1-x)^{101}-\frac {1}{100} (1-x)^{100} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \left ((1-x)^{99}-(1-x)^{100}\right ) \, dx\\ &=-\frac {1}{100} (1-x)^{100}+\frac {1}{101} (1-x)^{101}\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(567\) vs. \(2(23)=46\).
time = 0.00, size = 567, normalized size = 24.65 \begin {gather*} \frac {x^2}{2}-33 x^3+\frac {4851 x^4}{4}-\frac {156849 x^5}{5}+627396 x^6-10217592 x^7+140066157 x^8-1654114616 x^9+\frac {85600431378 x^{10}}{5}-157366449604 x^{11}+1298273209233 x^{12}-9696194317908 x^{13}+66026466069564 x^{14}-\frac {2062057324941768 x^{15}}{5}+\frac {4750096337812287 x^{16}}{2}-12666923567499432 x^{17}+62806829355518017 x^{18}-290505891817783026 x^{19}+\frac {12572449429225165403 x^{20}}{10}-5104603527655330314 x^{21}+19490304378320352108 x^{22}-70132813684308016488 x^{23}+238292173768273828749 x^{24}-\frac {19146258135816088501224 x^{25}}{25}+2331916055003241548226 x^{26}-6736646381120475583764 x^{27}+18488763007525700846649 x^{28}-48264408157576669898532 x^{29}+\frac {599857644244167183024612 x^{30}}{5}-284248449886557530554488 x^{31}+\frac {2570079734390957672096829 x^{32}}{4}-1386787891870780679371896 x^{33}+\frac {5720500053966970302409071 x^{34}}{2}-\frac {28206275157871771317939099 x^{35}}{5}+\frac {42585944846198556695711973 x^{36}}{4}-19237666204653402059452899 x^{37}+33300287699283081927474024 x^{38}-55246631151825154632274992 x^{39}+\frac {439428796464188236515924114 x^{40}}{5}-134109601422466453670901168 x^{41}+196374773511468735732390996 x^{42}-276016272695076305811040776 x^{43}+372502480574415750374856978 x^{44}-\frac {2414047083412492769871166152 x^{45}}{5}+601126348833940887359223192 x^{46}-719077854633508484642475024 x^{47}+826548729646668720118931889 x^{48}-913043842041304917057126672 x^{49}+\frac {24233705307512968006891237086 x^{50}}{25}-989130828878080326811887228 x^{51}+970109082168886474373197089 x^{52}-914479445566527094599669324 x^{53}+828502745555998906218503832 x^{54}-\frac {3606758093003645324155339152 x^{55}}{5}+603511770853123192467791538 x^{56}-485119509585285628395162576 x^{57}+374593512943317843600698196 x^{58}-277798460089394796889723848 x^{59}+\frac {989058310490690095822896114 x^{60}}{5}-135208860450519457389515112 x^{61}+88685381585824590330757224 x^{62}-55800482090690569716307824 x^{63}+\frac {134663663432573814416170293 x^{64}}{4}-\frac {97339302505596701018770224 x^{65}}{5}+\frac {21569504532490178066659311 x^{66}}{2}-5720500053966970302409071 x^{67}+\frac {11614348594417788189739629 x^{68}}{4}-1409398564020847755666003 x^{69}+\frac {3268857173695411601376612 x^{70}}{5}-289586448945460019391192 x^{71}+122384749256712270099849 x^{72}-49303368020068535591064 x^{73}+18914430223915181446722 x^{74}-\frac {172561788070239874568724 x^{75}}{25}+2393282266977011062653 x^{76}-787400226364730912388 x^{77}+245464847895078057708 x^{78}-72392559119475593544 x^{79}+\frac {201631839342385547403 x^{80}}{10}-5293662917568490696 x^{81}+1307276513180023617 x^{82}-302950588656028082 x^{83}+\frac {131419332012806607 x^{84}}{2}-\frac {66501348729372018 x^{85}}{5}+2503926751715004 x^{86}-436790467844808 x^{87}+70297408804833 x^{88}-10386185673864 x^{89}+\frac {7002807007378 x^{90}}{5}-171200862756 x^{91}+18815553757 x^{92}-1840869492 x^{93}+158372676 x^{94}-\frac {58975224 x^{95}}{5}+\frac {2980131 x^{96}}{4}-38808 x^{97}+\frac {3201 x^{98}}{2}-49 x^{99}+\frac {99 x^{100}}{100}-\frac {x^{101}}{101} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(501\) vs.
\(2(19)=38\).
time = 0.09, size = 502, normalized size = 21.83
method | result | size |
gosper | \(\text {Expression too large to display}\) | \(501\) |
default | \(\text {Expression too large to display}\) | \(502\) |
risch | \(\text {Expression too large to display}\) | \(502\) |
parallelrisch | \(\text {Expression too large to display}\) | \(502\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 501 vs.
\(2 (15) = 30\).
time = 0.38, size = 501, normalized size = 21.78 \begin {gather*} -\frac {1}{101} \, x^{101} + \frac {99}{100} \, x^{100} - 49 \, x^{99} + \frac {3201}{2} \, x^{98} - 38808 \, x^{97} + \frac {2980131}{4} \, x^{96} - \frac {58975224}{5} \, x^{95} + 158372676 \, x^{94} - 1840869492 \, x^{93} + 18815553757 \, x^{92} - 171200862756 \, x^{91} + \frac {7002807007378}{5} \, x^{90} - 10386185673864 \, x^{89} + 70297408804833 \, x^{88} - 436790467844808 \, x^{87} + 2503926751715004 \, x^{86} - \frac {66501348729372018}{5} \, x^{85} + \frac {131419332012806607}{2} \, x^{84} - 302950588656028082 \, x^{83} + 1307276513180023617 \, x^{82} - 5293662917568490696 \, x^{81} + \frac {201631839342385547403}{10} \, x^{80} - 72392559119475593544 \, x^{79} + 245464847895078057708 \, x^{78} - 787400226364730912388 \, x^{77} + 2393282266977011062653 \, x^{76} - \frac {172561788070239874568724}{25} \, x^{75} + 18914430223915181446722 \, x^{74} - 49303368020068535591064 \, x^{73} + 122384749256712270099849 \, x^{72} - 289586448945460019391192 \, x^{71} + \frac {3268857173695411601376612}{5} \, x^{70} - 1409398564020847755666003 \, x^{69} + \frac {11614348594417788189739629}{4} \, x^{68} - 5720500053966970302409071 \, x^{67} + \frac {21569504532490178066659311}{2} \, x^{66} - \frac {97339302505596701018770224}{5} \, x^{65} + \frac {134663663432573814416170293}{4} \, x^{64} - 55800482090690569716307824 \, x^{63} + 88685381585824590330757224 \, x^{62} - 135208860450519457389515112 \, x^{61} + \frac {989058310490690095822896114}{5} \, x^{60} - 277798460089394796889723848 \, x^{59} + 374593512943317843600698196 \, x^{58} - 485119509585285628395162576 \, x^{57} + 603511770853123192467791538 \, x^{56} - \frac {3606758093003645324155339152}{5} \, x^{55} + 828502745555998906218503832 \, x^{54} - 914479445566527094599669324 \, x^{53} + 970109082168886474373197089 \, x^{52} - 989130828878080326811887228 \, x^{51} + \frac {24233705307512968006891237086}{25} \, x^{50} - 913043842041304917057126672 \, x^{49} + 826548729646668720118931889 \, x^{48} - 719077854633508484642475024 \, x^{47} + 601126348833940887359223192 \, x^{46} - \frac {2414047083412492769871166152}{5} \, x^{45} + 372502480574415750374856978 \, x^{44} - 276016272695076305811040776 \, x^{43} + 196374773511468735732390996 \, x^{42} - 134109601422466453670901168 \, x^{41} + \frac {439428796464188236515924114}{5} \, x^{40} - 55246631151825154632274992 \, x^{39} + 33300287699283081927474024 \, x^{38} - 19237666204653402059452899 \, x^{37} + \frac {42585944846198556695711973}{4} \, x^{36} - \frac {28206275157871771317939099}{5} \, x^{35} + \frac {5720500053966970302409071}{2} \, x^{34} - 1386787891870780679371896 \, x^{33} + \frac {2570079734390957672096829}{4} \, x^{32} - 284248449886557530554488 \, x^{31} + \frac {599857644244167183024612}{5} \, x^{30} - 48264408157576669898532 \, x^{29} + 18488763007525700846649 \, x^{28} - 6736646381120475583764 \, x^{27} + 2331916055003241548226 \, x^{26} - \frac {19146258135816088501224}{25} \, x^{25} + 238292173768273828749 \, x^{24} - 70132813684308016488 \, x^{23} + 19490304378320352108 \, x^{22} - 5104603527655330314 \, x^{21} + \frac {12572449429225165403}{10} \, x^{20} - 290505891817783026 \, x^{19} + 62806829355518017 \, x^{18} - 12666923567499432 \, x^{17} + \frac {4750096337812287}{2} \, x^{16} - \frac {2062057324941768}{5} \, x^{15} + 66026466069564 \, x^{14} - 9696194317908 \, x^{13} + 1298273209233 \, x^{12} - 157366449604 \, x^{11} + \frac {85600431378}{5} \, x^{10} - 1654114616 \, x^{9} + 140066157 \, x^{8} - 10217592 \, x^{7} + 627396 \, x^{6} - \frac {156849}{5} \, x^{5} + \frac {4851}{4} \, x^{4} - 33 \, x^{3} + \frac {1}{2} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 501 vs.
\(2 (15) = 30\).
time = 0.56, size = 501, normalized size = 21.78 \begin {gather*} -\frac {1}{101} \, x^{101} + \frac {99}{100} \, x^{100} - 49 \, x^{99} + \frac {3201}{2} \, x^{98} - 38808 \, x^{97} + \frac {2980131}{4} \, x^{96} - \frac {58975224}{5} \, x^{95} + 158372676 \, x^{94} - 1840869492 \, x^{93} + 18815553757 \, x^{92} - 171200862756 \, x^{91} + \frac {7002807007378}{5} \, x^{90} - 10386185673864 \, x^{89} + 70297408804833 \, x^{88} - 436790467844808 \, x^{87} + 2503926751715004 \, x^{86} - \frac {66501348729372018}{5} \, x^{85} + \frac {131419332012806607}{2} \, x^{84} - 302950588656028082 \, x^{83} + 1307276513180023617 \, x^{82} - 5293662917568490696 \, x^{81} + \frac {201631839342385547403}{10} \, x^{80} - 72392559119475593544 \, x^{79} + 245464847895078057708 \, x^{78} - 787400226364730912388 \, x^{77} + 2393282266977011062653 \, x^{76} - \frac {172561788070239874568724}{25} \, x^{75} + 18914430223915181446722 \, x^{74} - 49303368020068535591064 \, x^{73} + 122384749256712270099849 \, x^{72} - 289586448945460019391192 \, x^{71} + \frac {3268857173695411601376612}{5} \, x^{70} - 1409398564020847755666003 \, x^{69} + \frac {11614348594417788189739629}{4} \, x^{68} - 5720500053966970302409071 \, x^{67} + \frac {21569504532490178066659311}{2} \, x^{66} - \frac {97339302505596701018770224}{5} \, x^{65} + \frac {134663663432573814416170293}{4} \, x^{64} - 55800482090690569716307824 \, x^{63} + 88685381585824590330757224 \, x^{62} - 135208860450519457389515112 \, x^{61} + \frac {989058310490690095822896114}{5} \, x^{60} - 277798460089394796889723848 \, x^{59} + 374593512943317843600698196 \, x^{58} - 485119509585285628395162576 \, x^{57} + 603511770853123192467791538 \, x^{56} - \frac {3606758093003645324155339152}{5} \, x^{55} + 828502745555998906218503832 \, x^{54} - 914479445566527094599669324 \, x^{53} + 970109082168886474373197089 \, x^{52} - 989130828878080326811887228 \, x^{51} + \frac {24233705307512968006891237086}{25} \, x^{50} - 913043842041304917057126672 \, x^{49} + 826548729646668720118931889 \, x^{48} - 719077854633508484642475024 \, x^{47} + 601126348833940887359223192 \, x^{46} - \frac {2414047083412492769871166152}{5} \, x^{45} + 372502480574415750374856978 \, x^{44} - 276016272695076305811040776 \, x^{43} + 196374773511468735732390996 \, x^{42} - 134109601422466453670901168 \, x^{41} + \frac {439428796464188236515924114}{5} \, x^{40} - 55246631151825154632274992 \, x^{39} + 33300287699283081927474024 \, x^{38} - 19237666204653402059452899 \, x^{37} + \frac {42585944846198556695711973}{4} \, x^{36} - \frac {28206275157871771317939099}{5} \, x^{35} + \frac {5720500053966970302409071}{2} \, x^{34} - 1386787891870780679371896 \, x^{33} + \frac {2570079734390957672096829}{4} \, x^{32} - 284248449886557530554488 \, x^{31} + \frac {599857644244167183024612}{5} \, x^{30} - 48264408157576669898532 \, x^{29} + 18488763007525700846649 \, x^{28} - 6736646381120475583764 \, x^{27} + 2331916055003241548226 \, x^{26} - \frac {19146258135816088501224}{25} \, x^{25} + 238292173768273828749 \, x^{24} - 70132813684308016488 \, x^{23} + 19490304378320352108 \, x^{22} - 5104603527655330314 \, x^{21} + \frac {12572449429225165403}{10} \, x^{20} - 290505891817783026 \, x^{19} + 62806829355518017 \, x^{18} - 12666923567499432 \, x^{17} + \frac {4750096337812287}{2} \, x^{16} - \frac {2062057324941768}{5} \, x^{15} + 66026466069564 \, x^{14} - 9696194317908 \, x^{13} + 1298273209233 \, x^{12} - 157366449604 \, x^{11} + \frac {85600431378}{5} \, x^{10} - 1654114616 \, x^{9} + 140066157 \, x^{8} - 10217592 \, x^{7} + 627396 \, x^{6} - \frac {156849}{5} \, x^{5} + \frac {4851}{4} \, x^{4} - 33 \, x^{3} + \frac {1}{2} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 561 vs.
\(2 (12) = 24\).
time = 0.10, size = 561, normalized size = 24.39 \begin {gather*} - \frac {x^{101}}{101} + \frac {99 x^{100}}{100} - 49 x^{99} + \frac {3201 x^{98}}{2} - 38808 x^{97} + \frac {2980131 x^{96}}{4} - \frac {58975224 x^{95}}{5} + 158372676 x^{94} - 1840869492 x^{93} + 18815553757 x^{92} - 171200862756 x^{91} + \frac {7002807007378 x^{90}}{5} - 10386185673864 x^{89} + 70297408804833 x^{88} - 436790467844808 x^{87} + 2503926751715004 x^{86} - \frac {66501348729372018 x^{85}}{5} + \frac {131419332012806607 x^{84}}{2} - 302950588656028082 x^{83} + 1307276513180023617 x^{82} - 5293662917568490696 x^{81} + \frac {201631839342385547403 x^{80}}{10} - 72392559119475593544 x^{79} + 245464847895078057708 x^{78} - 787400226364730912388 x^{77} + 2393282266977011062653 x^{76} - \frac {172561788070239874568724 x^{75}}{25} + 18914430223915181446722 x^{74} - 49303368020068535591064 x^{73} + 122384749256712270099849 x^{72} - 289586448945460019391192 x^{71} + \frac {3268857173695411601376612 x^{70}}{5} - 1409398564020847755666003 x^{69} + \frac {11614348594417788189739629 x^{68}}{4} - 5720500053966970302409071 x^{67} + \frac {21569504532490178066659311 x^{66}}{2} - \frac {97339302505596701018770224 x^{65}}{5} + \frac {134663663432573814416170293 x^{64}}{4} - 55800482090690569716307824 x^{63} + 88685381585824590330757224 x^{62} - 135208860450519457389515112 x^{61} + \frac {989058310490690095822896114 x^{60}}{5} - 277798460089394796889723848 x^{59} + 374593512943317843600698196 x^{58} - 485119509585285628395162576 x^{57} + 603511770853123192467791538 x^{56} - \frac {3606758093003645324155339152 x^{55}}{5} + 828502745555998906218503832 x^{54} - 914479445566527094599669324 x^{53} + 970109082168886474373197089 x^{52} - 989130828878080326811887228 x^{51} + \frac {24233705307512968006891237086 x^{50}}{25} - 913043842041304917057126672 x^{49} + 826548729646668720118931889 x^{48} - 719077854633508484642475024 x^{47} + 601126348833940887359223192 x^{46} - \frac {2414047083412492769871166152 x^{45}}{5} + 372502480574415750374856978 x^{44} - 276016272695076305811040776 x^{43} + 196374773511468735732390996 x^{42} - 134109601422466453670901168 x^{41} + \frac {439428796464188236515924114 x^{40}}{5} - 55246631151825154632274992 x^{39} + 33300287699283081927474024 x^{38} - 19237666204653402059452899 x^{37} + \frac {42585944846198556695711973 x^{36}}{4} - \frac {28206275157871771317939099 x^{35}}{5} + \frac {5720500053966970302409071 x^{34}}{2} - 1386787891870780679371896 x^{33} + \frac {2570079734390957672096829 x^{32}}{4} - 284248449886557530554488 x^{31} + \frac {599857644244167183024612 x^{30}}{5} - 48264408157576669898532 x^{29} + 18488763007525700846649 x^{28} - 6736646381120475583764 x^{27} + 2331916055003241548226 x^{26} - \frac {19146258135816088501224 x^{25}}{25} + 238292173768273828749 x^{24} - 70132813684308016488 x^{23} + 19490304378320352108 x^{22} - 5104603527655330314 x^{21} + \frac {12572449429225165403 x^{20}}{10} - 290505891817783026 x^{19} + 62806829355518017 x^{18} - 12666923567499432 x^{17} + \frac {4750096337812287 x^{16}}{2} - \frac {2062057324941768 x^{15}}{5} + 66026466069564 x^{14} - 9696194317908 x^{13} + 1298273209233 x^{12} - 157366449604 x^{11} + \frac {85600431378 x^{10}}{5} - 1654114616 x^{9} + 140066157 x^{8} - 10217592 x^{7} + 627396 x^{6} - \frac {156849 x^{5}}{5} + \frac {4851 x^{4}}{4} - 33 x^{3} + \frac {x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 501 vs.
\(2 (15) = 30\).
time = 0.44, size = 501, normalized size = 21.78 \begin {gather*} -\frac {1}{101} \, x^{101} + \frac {99}{100} \, x^{100} - 49 \, x^{99} + \frac {3201}{2} \, x^{98} - 38808 \, x^{97} + \frac {2980131}{4} \, x^{96} - \frac {58975224}{5} \, x^{95} + 158372676 \, x^{94} - 1840869492 \, x^{93} + 18815553757 \, x^{92} - 171200862756 \, x^{91} + \frac {7002807007378}{5} \, x^{90} - 10386185673864 \, x^{89} + 70297408804833 \, x^{88} - 436790467844808 \, x^{87} + 2503926751715004 \, x^{86} - \frac {66501348729372018}{5} \, x^{85} + \frac {131419332012806607}{2} \, x^{84} - 302950588656028082 \, x^{83} + 1307276513180023617 \, x^{82} - 5293662917568490696 \, x^{81} + \frac {201631839342385547403}{10} \, x^{80} - 72392559119475593544 \, x^{79} + 245464847895078057708 \, x^{78} - 787400226364730912388 \, x^{77} + 2393282266977011062653 \, x^{76} - \frac {172561788070239874568724}{25} \, x^{75} + 18914430223915181446722 \, x^{74} - 49303368020068535591064 \, x^{73} + 122384749256712270099849 \, x^{72} - 289586448945460019391192 \, x^{71} + \frac {3268857173695411601376612}{5} \, x^{70} - 1409398564020847755666003 \, x^{69} + \frac {11614348594417788189739629}{4} \, x^{68} - 5720500053966970302409071 \, x^{67} + \frac {21569504532490178066659311}{2} \, x^{66} - \frac {97339302505596701018770224}{5} \, x^{65} + \frac {134663663432573814416170293}{4} \, x^{64} - 55800482090690569716307824 \, x^{63} + 88685381585824590330757224 \, x^{62} - 135208860450519457389515112 \, x^{61} + \frac {989058310490690095822896114}{5} \, x^{60} - 277798460089394796889723848 \, x^{59} + 374593512943317843600698196 \, x^{58} - 485119509585285628395162576 \, x^{57} + 603511770853123192467791538 \, x^{56} - \frac {3606758093003645324155339152}{5} \, x^{55} + 828502745555998906218503832 \, x^{54} - 914479445566527094599669324 \, x^{53} + 970109082168886474373197089 \, x^{52} - 989130828878080326811887228 \, x^{51} + \frac {24233705307512968006891237086}{25} \, x^{50} - 913043842041304917057126672 \, x^{49} + 826548729646668720118931889 \, x^{48} - 719077854633508484642475024 \, x^{47} + 601126348833940887359223192 \, x^{46} - \frac {2414047083412492769871166152}{5} \, x^{45} + 372502480574415750374856978 \, x^{44} - 276016272695076305811040776 \, x^{43} + 196374773511468735732390996 \, x^{42} - 134109601422466453670901168 \, x^{41} + \frac {439428796464188236515924114}{5} \, x^{40} - 55246631151825154632274992 \, x^{39} + 33300287699283081927474024 \, x^{38} - 19237666204653402059452899 \, x^{37} + \frac {42585944846198556695711973}{4} \, x^{36} - \frac {28206275157871771317939099}{5} \, x^{35} + \frac {5720500053966970302409071}{2} \, x^{34} - 1386787891870780679371896 \, x^{33} + \frac {2570079734390957672096829}{4} \, x^{32} - 284248449886557530554488 \, x^{31} + \frac {599857644244167183024612}{5} \, x^{30} - 48264408157576669898532 \, x^{29} + 18488763007525700846649 \, x^{28} - 6736646381120475583764 \, x^{27} + 2331916055003241548226 \, x^{26} - \frac {19146258135816088501224}{25} \, x^{25} + 238292173768273828749 \, x^{24} - 70132813684308016488 \, x^{23} + 19490304378320352108 \, x^{22} - 5104603527655330314 \, x^{21} + \frac {12572449429225165403}{10} \, x^{20} - 290505891817783026 \, x^{19} + 62806829355518017 \, x^{18} - 12666923567499432 \, x^{17} + \frac {4750096337812287}{2} \, x^{16} - \frac {2062057324941768}{5} \, x^{15} + 66026466069564 \, x^{14} - 9696194317908 \, x^{13} + 1298273209233 \, x^{12} - 157366449604 \, x^{11} + \frac {85600431378}{5} \, x^{10} - 1654114616 \, x^{9} + 140066157 \, x^{8} - 10217592 \, x^{7} + 627396 \, x^{6} - \frac {156849}{5} \, x^{5} + \frac {4851}{4} \, x^{4} - 33 \, x^{3} + \frac {1}{2} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 12, normalized size = 0.52 \begin {gather*} -\frac {\left (100\,x+1\right )\,{\left (x-1\right )}^{100}}{10100} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 20, normalized size = 0.87 \begin {gather*} \frac {\left (1-x \right )^{101}}{10100}-\frac {x \left (1-x \right )^{100}}{100} \end {gather*}
Warning: Unable to verify antiderivative.
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